or little Big Bang

Equilibration Equilibration of of

Matter Near Matter Near QCD Critical QCD Critical

PointPointLarissa Bravina / Konrad Tywoniuk, Larissa Bravina / Konrad Tywoniuk, University of OsloUniversity of Oslo

Content

• Motivation. Why 40 AGeV?Motivation. Why 40 AGeV?• Conditions of thermal and chemical equilibriumConditions of thermal and chemical equilibrium• Statistical model of ideal hadron gasStatistical model of ideal hadron gas• Relaxation to equilibrium in central cellRelaxation to equilibrium in central cell• EOS of hot and dense matter in the cellEOS of hot and dense matter in the cell• Features of anisotropic flow around 40 AGeVFeatures of anisotropic flow around 40 AGeV• Summary and perspectivesSummary and perspectives

MotivationMotivation

Why 40 AGeV?Why 40 AGeV?

Equation of State

Critical point is located around 10-40 GeV (LQCD)

We have to explore this energy range to study the possible phase transition

QGP can be formed already at low energies

H. Stoecker, nucl-th/0506013 L. H. Stoecker, nucl-th/0506013 L. Bravina et al., PRC 60 (1999) 024904; 63 (2001) 064902Bravina et al., PRC 60 (1999) 024904; 63 (2001) 064902

Experimental IndicationsOnset of deconfinement

or

transition from baryon to meson dominated matter?

M. Gazdzicki, nucl-th/0512034 J. Cleymans et al., Phys. Lett. B 615, 50 M. Gazdzicki, nucl-th/0512034 J. Cleymans et al., Phys. Lett. B 615, 50

Central cell:Central cell:Relaxation to Relaxation to equilibrium equilibrium

Equilibration in the Central CellEquilibration in the Central Cell

Kinetic equilibrium:Kinetic equilibrium: Isotropy of velocity distributionsIsotropy of velocity distributions

Isotropy of pressureIsotropy of pressure

Thermal equilibrium: Thermal equilibrium: Energy spectra of particles are Energy spectra of particles are described by Boltzmann distributiondescribed by Boltzmann distribution

Chemical equlibrium:Chemical equlibrium: Particle yields are reproduced by SM with the same values of Particle yields are reproduced by SM with the same values of

Statistical model of ideal hadron gasStatistical model of ideal hadron gasinput values

output values

Multiplicity

Energy

Pressure

Entropy density

Pre-equilibrium StagePre-equilibrium Stage

Homogeneity of baryon matterHomogeneity of baryon matter Absence of flowAbsence of flow

The local equilibrium in the central zone is quite possible The local equilibrium in the central zone is quite possible

Kinetic EquilibriumKinetic Equilibrium

Isotropy of velocity distributionsIsotropy of velocity distributions

Isotropy of pressureIsotropy of pressure

Velocity distributions and pressure become isotropic at Velocity distributions and pressure become isotropic at t=8 fm/c t=8 fm/c (for 40 AGeV) (for 40 AGeV)

Thermal and Chemical EquilibriumThermal and Chemical Equilibrium

Energy spectraEnergy spectra Evolution of yieldsEvolution of yields

Thermal and chemical equilibrium seems to be reached...Thermal and chemical equilibrium seems to be reached...

STEADY STATESTEADY STATE

Negative net strangeness densityNegative net strangeness density

Net strangeness density in the central cell at 11 to 80 AGeV Net strangeness density in the central cell at 11 to 80 AGeV

Net strangeness in the cell is negative because of different interaction Net strangeness in the cell is negative because of different interaction cross sections for cross sections for Kaons Kaons andand antiKaons antiKaons withwith Baryons Baryons

Equation of StateEquation of StateT vs. energy, T vs. energy,

etc etc

Isentropic expansionIsentropic expansion

Expansion proceeds Expansion proceeds isentropicallyisentropically (with (with constant entropy constant entropy per baryon). This per baryon). This result supports result supports application of application of hydrodynamicshydrodynamics

EOS in the cellEOS in the cell

energy vs. baryon densityenergy vs. baryon density

temperature vs. energytemperature vs. energy

Beginning of temperature Beginning of temperature ”saturation””saturation”

Dense and hot equilibrated Dense and hot equilibrated (almost) matter is formed (almost) matter is formed

Infinite nuclear matter Infinite nuclear matter at normal nuclear at normal nuclear density and zero net density and zero net strangeness.strangeness.

EOS in the cellEOS in the cell

pressure vs. energypressure vs. energy

Elliptic flow of pions and protons at 40 AGeVElliptic flow of pions and protons at 40 AGeV

C. Alt et al. (NA49), PRC 68 (2003) 034903 C. Alt et al. (NA49), PRC 68 (2003) 034903 Signifi

cant d

ip at

mid

rapid

ity

Signifi

cant d

ip at

mid

rapid

ity

for p

roto

n flow

in ce

ntral e

vents

for p

roto

n flow

in ce

ntral e

vents

Elliptic flow of pions and protons at 40 AGeVElliptic flow of pions and protons at 40 AGeV

C. Alt et al. (NA49), PRC 68 (2003) 034903 C. Alt et al. (NA49), PRC 68 (2003) 034903

However, However, the dip at the dip at midrapidity midrapidity disappears if disappears if one uses the one uses the {2} or {4} {2} or {4} cumulant cumulant methodmethod

Elliptic flow of pions and protons at 40 AGeVElliptic flow of pions and protons at 40 AGeV

ConclusionsConclusions

Summary and perspectivesSummary and perspectives

• There is a kinetic equilibrium stage of hadron-There is a kinetic equilibrium stage of hadron-string matter in the central cell at t > 8 fm/cstring matter in the central cell at t > 8 fm/c

• The ratio P/e is approximately constant and The ratio P/e is approximately constant and equals 0.12 (AGS), 0.14 (40 AGeV), and 0.15 equals 0.12 (AGS), 0.14 (40 AGeV), and 0.15 (SPS & RHIC) => onset of saturation(SPS & RHIC) => onset of saturation

• Entropy per baryon ratio remains constant Entropy per baryon ratio remains constant during the time interval 8 fm/c < t < 20 fm/c. during the time interval 8 fm/c < t < 20 fm/c. This supports application of hydrodynamics This supports application of hydrodynamics

• Anisotropic flow at 40 AGeV : directed flow is Anisotropic flow at 40 AGeV : directed flow is nicely reproduced, while the situation with nicely reproduced, while the situation with elliptic flow remains an open question elliptic flow remains an open question

Applicability of different models